Here is the transfer function that needs to be transformed back into the time domain:
$$Y(s)=\frac{K_{2}e^{-\theta s}}{s(\tau_{1} s + 1)(\tau_{2} s + 1)}$$
Then would the response be: $$y(t) = K_{2}(t-\theta ) \Bigg(1-\frac{\tau_{1}e^{\frac{-(t-\theta)}{\tau_{1}}}-\tau_{2}e^{\frac{-(t-\theta)}{\tau_{2}}}}{\tau_{1}-\tau_{2}}\Bigg)$$
EDIT:
Ok, I'm pretty sure I am right now, but how the hell do I put something like this into matlab?
$$\mathcal{L}^{-1}(e^{-\theta s}) = \delta(t-\theta)$$ also known as the Dirac Delta function. The rest is pretty easy to solve as it appears to be a second order of a Type 1 oscillator.